"Are you ready now... to witness a power not seen for thousands of years?"
English: Vegeta
Japanese: Vejiita, Bejiita
Vegeta, the Prince of the Saiyans, is the other character that goes through a staggering development throughout Dragon Ball Z and GT. He begins as the proud, bitter, vicious prince of a near-dead race, driven by a nearly maddening need to avenge himself against Frieza, for destroying the Saiyan race, and against Goku, for besting him in combat. But, by the time GT comes to a close, his madness has passed, and he lives for something other than revenge... to protect his family. And I know what you're thinking... how the heck does that happen?!
Hundreds of fanfictions have explored the depth and breadth of Vegeta's personality, and many of them have proposed interesting and entirely plausible reasons for his 180 degree turnaround. Perhaps he had all tender feelings beaten out of him by Saiyan upbringing (since he is the only true Saiyan on the show, there is no information on the customs of the species as a whole), and spending time with emotionally-free Earthlings helped shatter that shell. Perhaps spending his youth in Frieza's service numbed him to feeling anything that could be considered "weak." I happen to think it's probably a mixture of those, and perhaps other, reasons.
Here's what we do know about Vegeta: at the start of Dragon Ball Z he was one of four Saiyans that survived the destruction of Vejiitasei (their home planet), the other three being Goku/Kakarott, Radditz, and Nappa. Now, Goku was raised human, so he doesn't really count. The other three were off-planet when Vejiitasei exploded, and were told by Frieza that it was a comet that collided with the planet. Vegeta never truly believed this, as he always suspected Frieza of foul play. Since Frieza was so much more powerful than anything else in creation, Vegeta decided not to face him up front. He bided his time, until some sort of advantage would surface.
That advantage appeared when he learned of the Dragon Balls of Earth via Radditz. Not caring about the death of his fellow Saiyan, he and Nappa hurried to Earth to wish for immortality (which would make both immune to Frieza's worst attacks). However, Vegeta discovered that Earth wouldn't be such an easy victory, for Kakarott, who went by the name "Goku," was actually powerful enough to stop him.
While Vegeta couldn't have honestly believed he was the most powerful warrior alive (considering Frieza and all his elite soldiers were also perfectly healthy), Goku was the first Saiyan Vegeta faced who could best him. And that fact burned the prince's ego like none other, and so Vegeta and Goku became arch rivals.
Vegeta decided to gamble that Namek had Dragon Balls as well, and raced to that planet to get a second chance at immortality. And on Namek, he faced an even worse defeat. He died against Frieza, who constantly mocked him the entire time, and even confessed to wiping the Saiyans out of existence. And when Vegeta was revived, he had to face a new truth: Frieza was dead, by the hands of the legendary Super Saiyan. And that Super Saiyan was Goku.
So blinding jealousy motivated Vegeta to seek the legendary power. Nonstop he pushed his body and mind to the very limit, his ultimate goal being to defeat Goku in battle, and claim his (in his opinion) destiny as the most powerful Saiyan to ever live. Yet, despite his torturous obsession, he found himself beginning to care for others... something he considered a weakness. We don't know exactly what happened, but he wound up the father of Bulma's baby. He didn't outwardly show any affection for Bulma, but he couldn't deny he cared for Future Trunks, who proved himself an able warrior. When Trunks died against Cell, Vegeta showed his feelings by flying into a vengeful rage. Someone had penetrated that stone heart.
And when Goku died against Cell, Vegeta found himself empty... without his rival, he thought he had nothing to live for.
But he did have something. He had Bulma, and even though Future Trunks returned to his own world, he still had the infant Trunks. And while he tried so hard to fight against the "weakness" that was building within him, he later confessed that he had a family, and a home... and enjoyed it. And he sacrificed his life in a desperate effort to destroy Buu, in order to save his loved ones (an absolutely incredible moment, if you haven't seen it).
Vegeta forever remained an arrogant, abrasive, emotionally-closed warrior, but even he wasn't immune to caring. He cared enough for his family to die for them... and more importantly, to live for them. Yes, he lived with Bulma in Capsule Corporation, and later they had a second child, Bra (who is definitely Daddy's little girl). He even grew to care for Goku, as their fierce rivalry transformed into (mostly) friendly competition.
More coming soon.